• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.245-252
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• 1996

The relative Nielsen number N(f;X,A) was introduced in 1986. It gives us a better, and ideally sharp, lower bound for the minimum number MF[f;X,A] of fixed points in the homotopy class of the map $f;(X,A) \to (X,A)$. Similarly, we also can think about the Nielsen map $f:(X,A) \to (X,A)$. Similarly, we also can be think about the Nielsen root theory. In this paper, we introduce a relative root Nielsen number N(f;X,A,c) of $f:(X,A) \to (Y,B)$ and show some basic properties.

• Journal of Ginseng Research
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• v.22 no.4
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• pp.299-303
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• 1998

To know possibility of raw ginseng production for white- and red-ginseng by direct-sowing culture, seeds were directly sowed or seedlings were transplanted at soil condition of sandy loam in ginseng field. After cultivation, the characters of 5-year-old ginseng were investigated. Number of survived plants was increased with increase the seeding quantity in direct-sowing culture, the survived plants in direct-sowing culture was higher than that of transplanting one. Rate of the numbers of survived plants to numbers of seeds sowed in plots of 134 or 90 seeds sowed per tan, 180 x 90cm area, inspire of high number of survived plant was high compared to that of transplanting culture. Occurrence rate of rusty root of ginseng in direct-sowing culture was low significantly compared to that of transplanting culture. Root yield showed in the order of 134, 268, 90 seeds sowed, the values of yield in direct-sowing culture were high obviously compared to that of transplanting one. Individual root weight was increased with decrease the seeding quantity, however, the root weight in plot of 90 seeds sowed showed almost equal the weight in transplanting culture. The number of usable raw ginseng for white- and red-ginseng was increased with decrease of the seeding quantity; the numbers were higher than that of transplanting culture remarkably. We concluded that optimum seedling rate in direct-sowing culture of ginseng was 90 to 134 seeds per tan considering the yield per area and production rate of large root.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.587-597
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• 2017

In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

• Korean Journal of Plant Resources
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• v.14 no.3
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• pp.183-187
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• 2001

In order to obtain basic information for breeding varieties of Alisma plantago which is suitable for the southern part of Korea, nine local varieties were grown and yield components of plant were observed from Jun. 1999 to Dec. 1999 at farm field of Chonnam Sunchon Korea. Alisma plantago cv. Sunwol showed higher dry root yield than the other varieties used in the experiment. It showed relatively higher length of plant height and lower numbers of floral axis. Therefore, it was concluded that Sunwol was the most suitable variety with high yield and low floral axis at the southern part of Korea. The heritabilities of all observed characters were estimated to be large. Dry root yield was shown highly significant positive correlations with plant height and numbers of leaves. Dry root yield, plant height and numbers of leaves were shown negative correlation with number of floral axis and nursery leaves.

• Korean Journal of Medicinal Crop Science
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• v.4 no.1
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• pp.38-46
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• 1996

These studies were conducted to know the any differences in growth characteristics and root quality due to flower color and culture periods in Chinese bellflower. White flowered lines had tendency of increasing in growth characters such as stem numbers, capsule numbers and seed yield per plant, plant height, and root characters such as root weight, root length and root diameter even though statistically not significant. No differences were observed in saponin and essential oil contents between them. Three years old plants had more stems and capsules per plants, root weight and root length than two years old plants while no difference in saponin and essential oil contents between them. Saponin content was gradually decreased while essential oil content was clearly lowed in the roots from plants cultured more than 3 years even though no differences in stem and capsule numbers per plant and plant height.

• The korean journal of orthodontics
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• v.49 no.2
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• pp.106-115
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• 2019

Objective: This study aimed to evaluate the effects of force loading on root damage caused by contact with temporary anchorage devices (TADs) during orthodontic treatment and to examine the repair process 4, 8, and 12 weeks after TAD contact by micro-computed tomography (CT). Methods: We enrolled 42 volunteers who required bilateral upper first premolar extractions. The experimental study design was as follows. For both first premolars, cantilever springs were placed, and then TADs were immediately inserted between the premolars of all volunteers. According to the removal order of the appliances, the participants were divided into the TAD group (Group T: n = 21, only TAD removal) and the spring group (Group S: n = 21, only spring removal). A splitmouth design was adopted in both groups as follows. For each volunteer, the left premolars were extracted 4, 8, or 12 weeks after TAD-root contact. The right premolars were extracted immediately after contact in both groups (Groups T-C and S-C) and used as positive controls. Resorption volumes and numbers of craters were determined by micro-CT. Results: The numbers of resorption craters were higher in Group T than in Group S at 8 and 12 weeks (p < 0.01). Crater volumes were higher in Group T than in Group S at 4 and 12 weeks (p < 0.01, both). Conclusions: Root injury was not completely repaired 12 weeks after root-TAD contact, even when the TADs were removed in cases of continuous force application.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.195-200
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• 2015

In this paper, we give the condition for the existence of the q-th roots of p-adic numbers in $\mathbb{Q}_p$ with an integer $q{\geq}2$ and (p, q) = 1. We have the conditions for the existence of the fifth root and the seventh root of p-adic numbers in $\mathbb{Q}_p$, respectively.

• Journal of the Korean Wood Science and Technology
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• v.39 no.5
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• pp.406-419
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• 2011

This study was carried out to offer basic information on the wood anatomy of domestic yellow-poplar (Liriodendron tulipifera L.), a new plantation species selected by Korea Forest Service as one of the promising hardwood and bioenergy sources of the future, through comparison of stem wood with root wood in the qualitative and quantitative features. In the qualitative anatomical features, growth rings were distinct in stem wood but relatively less distinct in root wood. And stem wood appeared to have pores in radial multiples of 2 to 5, sometimes clusters but root wood to have pores in radial multiples of 2 to 3, rarely clusters. And numbers of bars in scalariform perforation plates were somewhat numerous in vessel elements of root wood than in those of stem wood. Interestingly, on the other hand, more extraneous materials in the wood rays of tap root than in those of lateral root and stem were confirmed in the chemical composition analyses. In the quantitative anatomical features, pore densities were significantly greater but vessel elements were considerably narrower in stem wood than in root wood. Vessel elements and wood fibers of root wood were considerably longer than those of stem wood. Rays were somewhat more numerous in stem wood than in root wood, and only ray heights of stem wood were more or less greater in cell numbers but both ray heights and widths of stem wood were lower in dimension than those of root wood. The anatomical differences between stem wood and root wood were thought to be associated with different growth environments between the stem above ground and the root below ground.

• Journal of the Korean Wood Science and Technology
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• v.44 no.2
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• pp.157-165
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• 2016

This study investigated several anatomical characteristics of Paulownia tomentosa roots. The root wood was separated into three parts from stem base (top, middle, and base) at different positions below ground. Qualitative anatomical data suggested that the growth rings in earlywood and latewood were structurally different. Furthermore, the root wood vessels were found having 2 to 3 radial multiples and they were appeared in the form of clusters. In addition, some sheath cells and septate axial parenchyma were observed. Regarding the quantitative anatomical characteristics, vessel and ray numbers per $mm^2$, as well as ray width and height differed significantly among the top, middle, and base rood wood parts. However, there were no significant differences in vessel diameters, cell wall thickness, and width and length of wood fibers among those parts. The crystallinity of the root top part was slightly higher than that of the middle and base parts. Furthermore, the vessel numbers, ray numbers, and ray width and height in the near pith (NP) area were higher compared to those in the near bark (NB) area. However, the fiber width and fiber length at NP were lower than those at NB. Overall, this study demonstrated some significant differences in the anatomical characteristics of the top, middle, and base parts of root wood from Paulownia tomentosa.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.485-505
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• 2019

In 1935, D. H. Lehmer introduced and investigated generalized Euler numbers $W_n$, defined by $${\frac{3}{e^t+e^{wt}e^{w^2t}}}={\sum\limits_{n=0}^{\infty}}W_n{\frac{t^n}{n!}}$$, where ${\omega}$ is a complex root of $x^2+x+1=0$. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli and Euler numbers. These concepts can be generalized to the hypergeometric Bernoulli and Euler numbers by several authors, including Ohno and the second author. In this paper, we study more general numbers in terms of determinants, which involve Bernoulli, Euler and Lehmer's generalized Euler numbers. The motivations and backgrounds of the definition are in an operator related to Graph theory. We also give several expressions and identities by Trudi's and inversion formulae.